Within the last several years, numerous algorithms have been proposed for face recognition. As described in M. Turk and A. Pentland, “Eigenfaces for Recognition”, J. Cognitive Neuroscience, Vol. 3, No. 1, 1991, pp. 71-86 and in M. Turk and A. Pentland, “Face Recognition Using Eigenfaces”, Proc. IEEE Conf. on Computer Vision and Pattern Recognition, (1991), pp. 586-591. In 1991 Turk and Pentland developed the Eigenfaces method based on the principal component analysis (PCA) or Karhunen-loeve expansion which is described in L. Sirovich and M. Kirby, “Low-Dimensional Procedure for Characterization of Human Faces”, J. Optical Soc. Am., Vol. 4, 1987, pp. 519-524 and in M. Kirby and L. Sirovich, “Application of the KL Procedure for the Characterization of Human Faces”, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 12, No. 1, January 1990, pp. 103-108. The main idea of PCA is to find the vectors that best account for the distribution of face images within the entire image space.
The Eigenfaces technique yielded good performance in face recognition despite variations in the pose, illumination and face expressions. Recently in Yang J., Zhang, D., Frangi, A. F. “Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition”, IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 26, No(1), January 2004, pp. 131-137, Yang et al. proposed the two dimensional PCA (2DPCA), which has many advantages over PCA (Eigenfaces) method. It is simpler for image feature extraction, better in recognition rate and more efficient in computation. However it is not as efficient as PCA in terms of storage requirements, as it requires more coefficients for image representation.
Component Analysis Statistical projection methods, such as the eigenfaces method described by Turk and Pentland have been used widely. They have given good results for various face recognition databases. Recently Yang presented the 2DPCA method that forms the covariance matrix S from N training images Ai (where I=1 to N). Ai has m rows and n columns. The processing is performed in 2D rather than converting each image into a one dimensional vector of size m×n as in disclosed by Turk and Pentland.
The n×n S matrix is computed from
                    S        :=                              1            N                    ·                                    ∑                              i                =                1                            N                        ⁢                                          [                                                                            (                                                                        A                          i                                                -                                                  A                          _                                                                    )                                        T                                    ·                                      (                                                                  A                        i                                            -                                              A                        _                                                              )                                                  ]                            -                                                          (        1        )            where A is the mean matrix of all the N training images.
A set of k vectors V=[V1, V2 . . . Vk] of size n is obtained, so that the projection of the training images on V gives the best scatter. It was shown by Yang et al. that the vectors Vj (where j=1 to k) are the k largest eigenvectors of the covariance matrix S, corresponding to the largest eigenvalues. V is used for feature extraction for every training image Ai.
The projected feature vectors Y1, Y2, . . . Yk, whereYj,i=AiVj j=1, 2, . . . k, i=1, . . . N  (2)are used to form a feature matrix Bi of size m×k for each training image Ai. WhereBi=[Y1,i, Y2,i, . . . Yk,i] i=1, 2, . . . N  (3)The tested image is projected on V, and the obtained feature matrix Bt is compared with those of the training images.
The Euclidean distances between the feature matrix of the tested image and the feature matrices of the training images are computed. The minimum distance indicates the image to be recognized.
                              d          ⁡                      (                                          B                t                            ⁢                              B                i                                      )                          =                              ∑                          j              =              1                        k                    ⁢                                                                                    Y                                      j                    ,                    t                                                  -                                  Y                                      j                    ,                    i                                                                                      2                                              (        4        )            Where ∥Yj,t−Yj,i∥ denotes the distance between the two principle component vectors Yj,t, and Yj,i.